I would say 1 of two things.
1) Your battery might be wired incorrectly. Most trailers the white wire is negative. The red or black wire is usually positive. I would grab each wire at the battery and hand trace it until it either goes to the frame, or into a junction box.
2) You have a blown fuse or circuit breaker. Follow the positive battery wire from the battery post until it goes into the trailer. Somewhere on that wire is either a circuit breaker or a fuse holder.
If it's a fuse holder, try swapping in a known good fuse like the one for the tongue jack to see if anything changes. If it's a circuit breaker try wiring around it or look for a very small reset button.
Last thing is to open the fuse panel in the trailer and check the two big 40 amp reverse polarity fuses. It's possible that one of them is blown. In a pinch you can put in a smaller fuse like 25A and see if the lights come on. It's perfectly safe to put in a smaller fuse than designed, just don't put in a larger fuse.
Do you happen to have a multimeter or 12 volt test light?